Not being able to collapse is temporary (we hope) and are working on a change that we expect will allow collapsing.
.rpt Inspector Professional Suite and .rpt Inspector Enterprise Suite have a feature known as Report Playlists which allowed you to group as many reports as you wanted in each report playlist you created. Opening a report playlist would open the reports from various locations and even in the order in which you placed them.
Sounds like you would benefit from something like that in .rpt Inspector Online. Since adding / removing the same reports all the time isn’t ideal, perhaps having an ability to tag the reports that have been added and then having some sort of filter based on the tags might help.